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AP Physics 1: Algebra-Based Practice Quiz: Rotational Kinetic Energy

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 10 questions to check your progress.

Question 1 of 10

Which equation correctly describes the rotational kinetic energy, $K_{rot}$, of a rigid system with rotational inertia $I$ and angular velocity $\omega$?

All Questions (10)

Which equation correctly describes the rotational kinetic energy, $K_{rot}$, of a rigid system with rotational inertia $I$ and angular velocity $\omega$?

A) $K_{rot} = \frac{1}{2}I\omega^2$

B) $K_{rot} = I\omega$

C) $K_{rot} = \frac{1}{2}I^2\omega$

D) $K_{rot} = I\omega^2$

Correct Answer: A

Based on the provided content, the formula for rotational kinetic energy is given by the equation $K_{rot} = \frac{1}{2}I\omega^2$.

A rigid disk is rotating with angular velocity $\omega$ and has rotational kinetic energy $K$. If its angular velocity is doubled to $2\omega$ while its rotational inertia remains constant, what is its new rotational kinetic energy?

A) $\frac{1}{2}K$

B) $K$

C) $2K$

D) $4K$

Correct Answer: D

Rotational kinetic energy is given by $K_{rot} = \frac{1}{2}I\omega^2$. Since $K_{rot}$ is proportional to the square of the angular velocity ($\omega^2$), doubling the angular velocity will increase the kinetic energy by a factor of $(2)^2 = 4$.

A solid sphere is rolling without slipping on a horizontal surface. Which of the following statements best describes its total kinetic energy?

A) It is equal to its translational kinetic energy only.

B) It is equal to its rotational kinetic energy only.

C) It is the sum of its translational and rotational kinetic energies.

D) It is zero because the net force on the sphere is zero.

Correct Answer: C

The provided content states that the total kinetic energy of a rigid system is the sum of its rotational kinetic energy due to its rotation about its center of mass and the translational kinetic energy due to the linear motion of its center of mass.

Under which of the following conditions can a rigid system possess rotational kinetic energy while having zero translational kinetic energy?

A) When it is rolling without slipping down an incline.

B) When it is sliding without rotating on a frictionless surface.

C) When it is rotating about a fixed axis through its center of mass.

D) This scenario is physically impossible.

Correct Answer: C

The content states that a rigid system can have rotational kinetic energy while its center of mass is at rest. This occurs when it rotates about a fixed axis, meaning it has angular velocity but the linear velocity of its center of mass is zero, resulting in zero translational kinetic energy.

Two wheels, A and B, have the same mass. Wheel A has a larger rotational inertia than wheel B. If both wheels rotate with the same angular velocity, which statement is true about their rotational kinetic energies ($K_A$ and $K_B$)?

A) $K_A > K_B$

B) $K_A < K_B$

C) $K_A = K_B$

D) The relationship cannot be determined without knowing their radii.

Correct Answer: A

According to the formula $K_{rot} = \frac{1}{2}I\omega^2$, rotational kinetic energy is directly proportional to the rotational inertia ($I$) when the angular velocity ($\omega$) is constant. Since Wheel A has a larger rotational inertia ($I_A > I_B$) and the same angular velocity, it will have a greater rotational kinetic energy ($K_A > K_B$).

A flywheel is spinning in place on a frictionless axle, so its center of mass is at rest. Why does the flywheel possess kinetic energy?

A) Because it has potential energy that is converted to kinetic energy.

B) Because its center of mass has a non-zero velocity.

C) Because the individual points that make up the flywheel have linear speed.

D) Because the net force acting on the flywheel is non-zero.

Correct Answer: C

The provided content explains that a rigid system can have rotational kinetic energy while its center of mass is at rest 'due to the individual points within the rigid system having linear speed and, therefore, kinetic energy.' Even though the center of mass is stationary, the particles composing the flywheel are moving in circles and thus have kinetic energy.

A bowling ball rolls down a lane. Its motion is analyzed in terms of the movement of its center of mass and its rotation about the center of mass. The total kinetic energy of the ball is correctly described as the sum of which two quantities?

A) Gravitational potential energy and elastic potential energy.

B) Rotational kinetic energy and gravitational potential energy.

C) Translational kinetic energy of the center of mass and rotational kinetic energy about the center of mass.

D) The kinetic energy of the topmost point and the kinetic energy of the bottommost point.

Correct Answer: C

This question directly tests the principle from the provided content: 'The total kinetic energy of a rigid system is the sum of its rotational kinetic energy due to its rotation about its center of mass and the translational kinetic energy due to the linear motion of its center of mass.'

A solid sphere (Object 1) with rotational inertia $I$ rotates with angular velocity $\omega$. A hollow cylinder (Object 2) with rotational inertia $2I$ rotates with angular velocity $\frac{1}{2}\omega$. What is the ratio of the rotational kinetic energy of Object 2 to Object 1 ($K_2 / K_1$)?

A) 1/4

B) 1/2

C) 1

D) 2

Correct Answer: B

The kinetic energy for each object is: $K_1 = \frac{1}{2}I\omega^2$. For Object 2, $K_2 = \frac{1}{2}(2I)(\frac{1}{2}\omega)^2 = \frac{1}{2}(2I)(\frac{1}{4}\omega^2) = \frac{1}{4}I\omega^2$. The ratio is $K_2 / K_1 = (\frac{1}{4}I\omega^2) / (\frac{1}{2}I\omega^2) = \frac{1/4}{1/2} = 1/2$.

The rotational kinetic energy of a rigid body is dependent on which two physical quantities?

A) Mass and linear velocity

B) Rotational inertia and angular velocity

C) Torque and angular acceleration

D) Angular momentum and radius

Correct Answer: B

The formula $K_{rot} = \frac{1}{2}I\omega^2$ explicitly shows that rotational kinetic energy ($K_{rot}$) is a function of the body's rotational inertia ($I$) and its angular velocity ($\omega$).

A spinning top is rotating about its vertical axis with its tip fixed at a single point on the ground. As it slows down due to friction, what happens to its rotational kinetic energy?

A) It increases because its rotational inertia increases.

B) It remains constant because energy is conserved in a closed system.

C) It decreases because its angular velocity decreases.

D) It is converted entirely into translational kinetic energy.

Correct Answer: C

The top's energy is primarily rotational. As friction does negative work on the system, its angular velocity ($\omega$) decreases. According to the equation $K_{rot} = \frac{1}{2}I\omega^2$, a decrease in $\omega$ (assuming $I$ is constant) will lead to a decrease in rotational kinetic energy. This energy is dissipated as heat.